My elderly parents made me their POA. Should I be adding my name to their finances so that I can handle their affairs?

Be aware that Power of Attorney ends with death. It will do you no good after your parents are gone.

Laura,

Adding, with your parents' consent, your name as POD is a good idea, because it will avoid probate and the costs associated with that. However, that will work only with the savings account, and not the home. If you attempt to have a new deed drafted adding additional co-owners, that may well trigger an immediate federal gift tax obligation, at least, because none of you children contributed to the purchase of the home, I'll bet. Talk to a local attorney about this.

Thank you so much for your input. Now, I am wondering if I should also add my name, as well as my siblings, to the deed on their home. I have been reading on-line that by having beneficiaries names added to their assets as POD; that after their death, things will not have to go through probate and things will not get tied up in court. They do not have many assets, their home, which is worth around $125,000 and a savings account for around $30,000. Any ideas on this?

If they are unable or have tired of keeping their own "books," yes, you will have to become a "signer" on their bank accounts. This means that they are allowing you to sign for them, but you are not financially responsible for the accounts. (this should be the understanding on all accounts that you have access to.)
Also, sign up for online banking. This has saved my life. I can pay most bills online, keep track of Mom's accts., and move funds from one account to another when she asks. It is also a good way to see if someone is illegally accessing their acounts or if their spending has become erratic.
good luck
PS: do you have a medical POA too?